Simulation of an Orographic Precipitation Event during IMPROVE-2. Part II: Sensitivity to the Number of Moments in the Bulk Microphysics Scheme

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1 FEBRUARY 2010 M I L B R A N D T E T A L. 625 Simulation of an Orographic Precipitation Event during IMPROVE-2. Part II: Sensitivity to the Number of Moments in the Bulk Microphysics Scheme J. A. MILBRANDT Meteorological Research Division, Environment Canada, Dorval, Quebec, Canada M. K. YAU McGill University, Montreal, Quebec, Canada J. MAILHOT, S.BÉLAIR, AND R. MCTAGGART-COWAN Meteorological Research Division, Environment Canada, Dorval, Quebec, Canada (Manuscript received 30 June 2009, in final form 17 August 2009) ABSTRACT This is the second in a series of papers examining the behavior of the Milbrandt Yau multimoment bulk microphysics scheme for the simulation of the December 2001 case of orographically enhanced precipitation observed during the second Improvement of Microphysical Parameterization through Observational Verification Experiment (IMPROVE-2) experiment. The sensitivity to the number of predicted moments of the hydrometeor size spectra in the bulk scheme was investigated. The triple-moment control simulations presented in Part I were rerun using double- and single-moment configurations of the multimoment scheme as well the single-moment Kong Yau scheme. Comparisons of total precipitation and incloud hydrometeor mass contents were made between the simulations and observations, with the focus on a 2-h quasi-steady period of heavy stratiform precipitation. The double- and triple-moment simulations were similar; both had realistic precipitation fields, though generally overpredicted in quantity, and had overprediction of snow mass and an underprediction of cloud water aloft. Switching from the triple- to singlemoment configuration resulted in a simulation with a precipitation pattern shifted upwind and with a larger positive bias, but with hydrometeor mass fields that corresponded more closely to the observations. Changing the particular single-moment scheme used had a greater impact than changing the number of moments predicted in the same scheme, with the Kong Yau simulations greatly overpredicting the total precipitation in the lee side of the mountain crest and producing too much snow aloft. Further sensitivity tests indicated that the leeside overprediction in the Kong Yau runs was most likely due to the combination of the absence of the latent heat effect term in the diffusional growth rate for snow combined with the assumption of instantaneous snow melting in the scheme. 1. Introduction Bulk microphysics schemes (BMSs) play an important role in high-resolution three-dimensional (3D) models and are becoming more commonly used in operational numerical weather prediction. There have been numerous sensitivity studies investigating the effects of varying the number of hydrometeor categories, the treatment of particle size distributions, and the mass Corresponding author address: Dr. Jason Milbrandt, 2121 Trans- Canada Highway, 5th floor, Dorval, QC H9P 1J3, Canada. jason.milbrandt@ec.gc.ca diameter and fall velocity relations (e.g., McCumber et al. 1991; Ferrier et al. 1995; Gilmore et al. 2004; Colle et al. 2005). In contrast, there has been comparatively less research on the sensitivity of BMSs to the number of predicted moments of the size distributions despite the importance of this topic for high-resolution modeling. Milbrandt and Yau (2005a) showed that the computation of instantaneous growth rates and the sedimentation of hydrometeors were greatly improved when the number of prognostic moments increased. The explicit simulation of deep convection is highly sensitive to whether a one- or a two-moment scheme is employed (Meyers et al. 1997; Milbrandt and Yau, 2006a; Milbrandt and Yau 2006b, DOI: /2009MWR3121.1

2 626 M O N T H L Y W E A T H E R R E V I E W VOLUME 138 hereinafter MY06b). A similar sensitivity was also shown by Reisner et al. (1998) for the simulation of supercooled cloud water, whose removal due to deposition and/or riming depends strongly on the treatment of the ice-phase categories. Since increasing computing power makes running models with high-moment schemes feasible, further examination of the importance of the number of predicted moments in cloud-resolving (or convection permitting) models is merited. The multimoment scheme of Milbrandt and Yau (2005a, hereinafter MY05a; Milbrandt and Yau (2005b, hereinafter MY05b) is ideally suited for such a study because it allows the choice between one, two, or three prognostic moments in each of the six hydrometeor categories. 1 Milbrandt and Yau (2006a; MY06b) simulated a case of severe convection and found that reducing the number of moments from three to two changed the proportion of frozen and liquid precipitation at the surface. This was primarily due to the problem of excessive size sorting that exists in double-moment schemes that hold the spectral dispersion parameter constant. This problem was overcome by a triple-moment scheme. It was also demonstrated that the adoption of a diagnostic relation for this shape parameter in a double-moment BMS can nearly reproduce the results of the triplemoment control run (see MY06b). The results changed dramatically, however, when a single-moment BMS was used, with the storm structures, the precipitation, and the storm propagation speed being very different between the single-moment and multimoment runs. Likewise, changes to the parameters in the size distributions in the single-moment version led to notable changes in the simulations. This is in agreement with results of Gilmore et al. (2004) and van den Heever and Cotton (2004). MY06b showed that there was a dramatic improvement to the storm structure and precipitation pattern compared to radar observations in moving from a single- to a double-moment scheme, while the change was marginal when moving to a triple-moment scheme. To understand how the results from MY06b may vary with different types of weather systems, it is the goal of this paper to examine the sensitivity of the number of predicted moments in the context of an orographic heavy precipitation event that occurred on December 2001 over the Oregon Cascades. The control simulation using the triple-moment MY05a,b scheme reported in Milbrandt et al. (2008, hereinafter Part I) will be compared with runs using the corresponding double- and single-moment versions. For comparison, 1 For the cloud droplet category, only single- and double-moment options are available. a different single-moment BMS is also included in this study. The December 2001 case was observed during the second Improvement of Microphysical Parameterization through Observational Verification Experiment (IMPROVE-2) field campaign (Stoelinga et al. 2003). An overview is given in Part I. The triple-moment simulation was shown to produce too much snow mass while underpredicting the vertical extent of pockets of cloud water on the windward side of the mountains. However, the quantitative precipitation forecast (QPF) was quite reasonable, though generally overpredicted in terms of accumulated amounts, and was similar to that in Garvert et al. (2005a, hereinafter G05a; Garvert et al. (2005b, hereinafter G05b) using the single-moment 2 Reisner-2 BMS [Reisner et al. (1998), with modifications described in Thompson et al. (2004)]. One notable difference, however, was that the simulations described in Part I did not exhibit the pronounced overprediction of precipitation in the lee of the Cascade crest that were shown in the simulations of G05a,b. The organization of this paper is as follows. The next section gives an overview of the modeling setup and the various BMSs used. In section 3, the results from the sensitivity tests are presented, with comparisons to the simulated fields of vertical motion, precipitation, and hydrometeor mass contents. Section 4 provides a discussion of the differences between the simulations using the various schemes as well as the results from two additional sensitivity experiments that examine the leeside precipitation. Concluding remarks are given in section Overview of sensitivity tests Table 1 summarizes the four schemes used in the simulations discussed in this paper. All model conditions were identical to the control simulation (from Part I), hereinafter referred to as MY-3. The modified analyses from the National Centers for Environmental Prediction- Aviation model were used to initialize the limited-area configuration of the Canadian Global Environmental Multiscale (GEM) model (see Part I for details) on a coarse-resolution domain (36-km grid spacing) for a 36-h simulation (0000 UTC 13 December 1200 UTC 14 December 2001). The model was then successively nested to grids with 12-, 4-, and 1-km horizontal grid spacings (see Fig. 1 in Part I). The double- and singlemoment runs are termed MY-2 and MY-1, respectively. 2 The Reisner-2 scheme is single moment for all categories except ice, which is double moment. Since ice did not appear to play a major role in the G05a,b simulations, the Reisner-2 scheme is considered here to be essentially a single-moment scheme.

3 FEBRUARY 2010 M I L B R A N D T E T A L. 627 TABLE 1. Schemes configurations used in the sensitivity runs for experiment set 1. Simulation Microphysics scheme Treatment of size distribution parameters MY-3 MY05a,b, triple-moment version Fully prognostic MY-2 MY05a,b, double-moment version Diagnostic-a x ; prognostic N Ti, N Tc, N 0,r, N 0,s, N 0,g, N 0,h MY-1 MY05a,b, single-moment version Fixed a x ; diagnostic N Ti ; fixed N Ti, N Tc, N 0,r, N 0,s, N 0,g, N 0,h KY KY97 (single moment) Fixed a x ; diagnostic N Ti ; fixed N 0,r, N 0,i s, N 0,g Details are given in the appendix. All versions of the MY05a,b scheme include six hydrometeor categories: cloud, rain, ice, snow, graupel, and hail. Throughout this article hereafter, references to bulk scheme hydrometeor categories will be italicized to distinguish them from real particles. Simulations using a different single-moment BMS, described in Kong and Yau (1997, hereinafter KY97) and Misra et al. (2000) are also included in this study and are referred to as the KY runs. This scheme has two liquid categories, cloud and rain, and two ice-phase categories, a hybrid pristine ice snow category referred to in this paper as snow (but called ice in KY97), and a graupel category (which behaves as hail for large mixing ratios). The KY97 scheme was readily available in the GEM model for simulations to be directly compared with the MY-x runs (MY-1, MY-2, and MY-3). 3. Results a. Vertical motion Vertical motion (w) is one of the most important controlling parameters driving the microphysics. Vertical cross sections of the instantaneous fields of w at 0000 UTC 14 December 2001 from the four 1-km runs are shown in Fig. 1. The w fields upwind of the Cascade crest are very similar for all runs. The patterns of standing waves were quasistationary during the entire period of stratiform precipitation, UTC (G05a; Woods et al. 2005). The vertical velocity pattern along leg 2 of the P-3 flight were similar to the observed pattern but with reduced magnitudes (see Fig. 11 in Part I). The forcing due to vertical motion, therefore, was largely unaltered by the change in scheme. The region of upward motion on the lee side of the crest, on the other hand, is notably larger for MY-1 than MY-2 and MY-3 and even larger for KY, but these differences do not affect the forcing upwind of this region. b. Precipitation The 18-h ( UTC) accumulated precipitation fields from the 4- and 1-km simulations were compared to rain gauge measurements. Figure 2 shows the results from the 4-km runs, together with the 145 rain gauge observations, with the 1-km simulation results shown in Fig. 3. For the 4-km runs, the MY-3 (Fig. 2a) and MY-2 (Fig. 2b) simulations exhibited similar precipitation patterns. The precipitation magnitudes were overpredicted in general, but the reduction in values in the Willamette value and the locations of the local maxima along the upwind side were reasonably well simulated. The reduced precipitation on the lee side of the Cascades was also captured. The pattern for MY-1 (Fig. 2c) was similar though the overprediction was even larger. The 4-km KY simulation (Fig. 2d) was notably different from the MY-x runs in that it exhibited a distinct overprediction in the region immediately on the lee side of the cascade crest. Each of the 1-km runs (Fig. 3) where qualitatively similar to the corresponding 4-km runs but with more variability in regions of complex orography, particularly along the windward side of the Cascades. Scatterplots (Fig. 4) of the observed versus simulated (nearest grid point to rain gauge) precipitation totals indicate a general overprediction (east of the coastal mountains) in all of the simulations, though there is slightly more scatter in MY-1 and KY. The bias scores for the 4-km runs are shown in Fig. 5, where the bias is calculated as Bias 5 H FA H 1 M, (1) for a range of precipitation thresholds (from 0.1 to 50 mm) where H, FA, and M are the number of hits, false alarms, and misses, respectively, for all of the gauges. For the lower precipitation threshold values (,30 mm), all runs have a slight positive bias, with MY-1 being slightly better (less) than the other runs. The biases increase with the threshold value for all of the runs and for the higher threshold values (.40 mm), MY-3 has the least bias and KY the greatest. The precipitation difference fields in the 4-km runs, plotted in Fig. 6, show that there is a larger systematic difference between MY-3 and MY-1 (Fig. 6b) than between MY-3 and MY-2 (Fig. 6a). The regions of these differences are linked to terrain features and thus to regions of quasi-stationary forcing (see Fig. 1). For example, the precipitation totals for MY-1 were notably larger than MY-3 along the coast and the windward slopes but lower in the Willamette Valley and lee side of the crest (Fig. 6b). For KY (Fig. 6c), there was an

4 628 M O N T H L Y W E A T H E R R E V I E W VOLUME 138 FIG. 1. Vertical motion (m s 21 ) at (left) 0000 UTC from 1-km simulations along vertical cross section indicated by the dashed line in Fig. 2a and (right) along leg 2 of the P-3 flight, indicated by dotted line in Fig. 2a for (a),(b) MY-3, (c),(d) MY-2, (e),(f) MY-1, and (g),(h) KY. Solid (dashed) contours denote upward (downward) motion with contours every 0.5 m s 21 (0 m s 21 contour not shown). Upward motion is shaded. apparent downwind shift in the precipitation relative to MY-3, indicated by a reduction (increase) along the coast and upwind slope (valley and lee side) with the most conspicuous difference along the immediate lee side where the KY values were over 80 mm larger. The simulations G05a,b exhibited a similar leeside overprediction. The reasons for this difference between the MY-x and the KY and G05a,b runs are examined in section 4. c. Hydrometeor mass fields Following from Part I, the time-averaged ( UTC) vertical cross sections of the mass contents, Q x, of each hydrometeor category x for MY-3, MY-2, MY-1, and KY are displayed in Figs. 7 10, respectively. The mean and peak hydrometeor mass contents for each run along the P-3 and Convair-580 flight legs are summarized in Tables 2 4 (see Part I for details). The cross sections of the mass fields for all categories in MY-2 (Fig. 8) are very similar to those of MY-3 (Fig. 7). The average and peak cloud water (Table 2) and snow (Tables 3 and 4) along the flight legs vary only slightly between MY-2 and MY-3. The similarity between MY-2 and MY-3 is also found for the total number concentrations and mean-mass diameters (not shown). On the other hand, there are several differences between MY-1 and MY-3 that merit attention. The vertical extent of the cloud field in MY-1 (Fig. 9a) is greater than MY-3 (Fig. 7a), particularly over the ocean. Upwind of the cascades in the cross sections depicted in the figures, Q c, exceeds 0.60 g m 23 at 700 hpa for MY-1 while it is near 0.40 g m 23 for MY-3. At the levels of the P-3 north south flight legs; however, Q c in MY-1 is only

5 FEBRUARY 2010 M I L B R A N D T E T A L. 629 FIG. 2. The 18-h accumulated precipitation (mm; 1400 UTC 13 Dec 0800 UTC 14 Dec 2001) from the 4-km simulations for (a) MY-3, (b) MY-2, (c) MY-1, and (d) KY. Circles denote rain gauges, with observed quantities indicated by the same shading scale as for the simulation values. Contours denote elevations of 1500 and 2000 m. Dashed, dotted, and solid arrows in (a) denote locations of vertical cross sections for Figs. 1a,c,e,g; Figs. 1b,d,f,h; and Figs. 6 9, 12, 13, respectively. slightly greater than MY-3 (Table 2). The rain mass field for MY-1 (Fig. 9b) is similar in spatial distribution but slightly lower in quantity when compared to MY-3 (Fig. 7), in agreement with the smaller accumulated precipitation in the former. There is considerably more ice (Fig. 8c) but less snow (Fig. 8d) in MY-1 than in MY-3 (Figs. 7b,d). The peak Q i in MY-1 exceeds 0.1 g m 23 at 300 hpa but is an order of magnitude less in MY-3. The largest values of Q s are near 700 hpa with the peak amount between 0.20 and 0.40 g m 23 for MY-1, while it exceeds 1.5 g m 23 for MY-3. Along both the Convair- 580 flight legs (Table 3) and the P-3 return flight leg (Table 4), the snow mass in MY-1 was closer to the observations than for MY-3 and MY-2, although all runs have more than the observed values. Note that the mass contents are much lower for ice than snow in the MY-x runs, thus the total ice 1 snow mass content is lower for MY-1 than MY-3. Hence, the extra ice mass in MY-1 does not balance the lower snow mass. The peak mass contents of the graupel field for MY-1 are similar to that of MY-3, though the vertical extent in MY-1 is larger, corresponding to a greater availability of cloud water for accretion. As in the MY-3 runs, there was no hail in the MY-1 simulations. There are both similarities as well as notable differences between the hydrometeor fields from the MY-1 and KY runs (Figs. 9 and 10). The cloud field in KY (Fig. 10a) is much deeper than MY-2 and MY-3 and with larger mass contents, similar to MY-1. It extends above 400 hpa in KY and a large region of Q c g m 23 is located over the windward side of the Cascades. Thus, KY and MY-1 predict the presence of appreciable

6 630 M O N T H L Y W E A T H E R R E V I E W VOLUME 138 FIG. 3. As in Fig. 2, but for the 1-km simulations. amounts of liquid water at the levels of the P-3 flight legs over the windward slope better than the multimoment runs, although the amounts were overpredicted (Table 4). On the other hand, the rain field in KY (Fig. 10b) has greater quantities than MY-1 (Fig. 9b) throughout most of the region. Also, there is a region with large Q r values on the immediate lee side of the crest, corresponding directly to the excessive precipitation at that location (Figs. 2d and 3d). The pattern of the snow field in KY (Fig. 10d) is closer to MY-2 (Fig. 8d) and MY-3 (Fig. 7d) than MY-1 (Fig. 9d), with a similar overprediction at the levels of the Convair-580 (Table 4) and at the lower levels of the P-3 return flight (Table 4). Unlike the MY-x runs, only a trace amount of graupel was simulated in KY (Fig. 10c) despite the abundance of cloud water available for riming (Fig. 10a). This is due to the strict conditions for conversion of snow to graupel in the KY scheme, which was designed to treat graupel as a hybrid graupel hail category. 4. Discussion a. Reduction to double-moment (MY-3 versus MY-2) The fact that the MY-2 configuration produced similar results to the MY-3 control run indicates that the diagnostic approach to treating the spectral dispersion parameter, a (see the appendix), allows MY-2 to reproduce most of the effects of the added variability in the particle size distributions in the full triple-moment scheme, at least with regard to the resulting simulated precipitation and hydrometeor mass fields for this case. MY-3, however, had slightly larger values of equivalent reflectivity, Z e (see Part I) than MY-2 (not shown) in certain regions such as in the Willamette Valley, which is attributable to the larger contribution to Z e from rain in MY-3. Thus, even though the magnitude of Q r was larger in MY-2 (Fig. 8b), the value of a r diagnosed in MY-2 was larger than the prognostic value in MY-3, resulting in a narrower rain spectrum in MY-2 and hence

7 FEBRUARY 2010 M I L B R A N D T E T A L. 631 FIG. 4. Scatterplots of rain gauge vs model (nearest grid point to gauge) for 18-h accumulated precipitation ( UTC) for the 4-km (solid circles) and 1-km (open diamonds) simulations for (a) MY-3, (b) MY-2, (c) MY-1, and (d) KY. lower reflectivity (due to a reduced contribution from the larger diameters). For the most part, however, there is very little sensitivity between MY-2 and MY-3 for this case. Note that other two-moment configurations, such as a fixed-a x approach may produce results different from our MY-2 runs, as was the case found in MY06b. of severe convection. This difference in sensitivity between multimoment and single-moment is likely due in part to a higher importance, in the simulation of deep convection, of rain and hail for which size-sorting plays an important role (MY06b). There is also a stronger b. Reduction to single-moment (MY-3 versus MY-1) In terms of the total precipitation, the scatterplots (Fig. 4), biases (Fig. 5), and difference fields (Fig. 6) indicate that there is a larger effect in reducing the bulk scheme to single-moment than to double-moment for this case. Specifically, the general overprediction in the control run is worse for MY-1, with areas along the coast and upwind slope having over 20 mm more precipitation (Fig. 6b). The overall precipitation pattern, however, is not changed dramatically. This result is in contrast to MY06b, who showed that reducing the number of moments from three to one resulted in very different (less realistic) simulations of precipitation, both quantitatively and in terms of the spatial distribution, for a case FIG. 5. Bias score for the 18-h accumulated precipitation of the 4-km simulations against the rain gauge values for various precipitation threshold values.

8 632 M O N T H L Y W E A T H E R R E V I E W VOLUME 138 FIG. 6. Differences in the 18-h accumulated precipitation (mm; UTC) between the following 4-km simulations and MY-3: (a) MY-2, (b) MY-1, and (c) KY. Solid (dashed) contours denote positive (negative) values; contours are 5, 10, 20, 40, 60, and 80 mm. Shading denotes orographic height, with intervals of 500 m. feedback of changes to the microphysics to the storm dynamics for deep convection compared a case with strong large-scale forcing with orographic enhancement. The simulated hydrometeor fields aloft for the IMPROVE-2 case were quite sensitive to the change in the number of prognostic moments, in particular the mass fields of ice and snow. The fact that the ice mass field in MY-1 (Fig. 9c) was much greater than in MY-3 and MY-2 can be attributed to the way the total ice number concentration, N Ti, was prescribed in MY-1 (see the appendix). First, in MY-1 N Ti was prescribed using the Cooper (1986) formulation, which yields larger ice concentrations than the Meyers et al. (1992) parameterization for heterogeneous (deposition-condensation freezing) nucleation, which is the dominant mechanism for ice initiation in MY-2 and MY-3 at water supersaturation for temperatures between 2308 and 2458C (Thompson et al. 2004). This temperature range approximately corresponds to the layer between approximately 400 and 300 hpa for this case (Fig. 7). Thus, for a given Q i, the total surface area of the ice will effectively be larger and the depositional growth rate greater. Second, the rate of conversion of ice to snow will also be smaller in MY-1 because there is no conversion to snow via ice aggregation since N Ti is not prognosed in the single-moment version [see Eqs. (42) (45) in MY05b]. Furthermore, the conversion to snow by ice growing through deposition and riming to the size of a snow embryo is smaller because the large N Ti from Cooper (1986) results in a smaller ice diameter for a given mass content. Unfortunately there were no in situ hydrometeor observations at 400 hpa (;7 km MSL) or higher for this case, thus it is uncertain which scheme best simulated the fields of small crystals at upper levels. The reason for the lower quantities of snow mass in MY-1 relative to MY-3 and MY-2 is less obvious. The fact that there is less conversion of ice to snow is presumably a factor. However, it should be possible for the total snow mass to attain large values via deposition alone, even if less snow is initiated from ice. It is apparent that the reduction to single moment has a notable impact on the simulated snow field in the current configuration of the MY05 scheme. The sensitivity to the depositional growth rate of snow is discussed below. The deeper pockets of cloud in MY-1 are consistent with the smaller values in snow mass, since excess snow results from large depositional growth rates and the depletion of water vapor that would otherwise be available for condensation. Conversion of snow to graupel (a sink for snow) does not appear to play a significant role in changing the snow fields between MY-1 and MY-3 since the graupel mass fields are similar, though a budget study would be required to determine this definitively.

9 FEBRUARY 2010 M I L B R A N D T E T A L. 633 FIG. 7. Vertical cross sections of time-averaged ( UTC, every 15 min) hydrometeor mass contents (Q x ;gm 23 ) from 1-km MY-3 simulation for (a) cloud, (b) ice and rain, (c) graupel, and (d) snow along cross section indicated by dashed line in Fig. 2a. Dashed contours for ice in (b) are 0.001, 0.01, and 0.1 g m 23. The vertical axis is pressure (hpa). North south flight legs of the P-3 are indicated in (a); flight legs from the Convair-580 and the return flight of the P-3 are indicated in (d). (Reproduced from Part I, with permission.) c. Sensitivity of the single-moment schemes (MY-1 versus KY) The simulated precipitation with KY in the GEM model was qualitatively similar to that of G05a,b with the Reisner-2 scheme in the fifth-generation Pennsylvania State University National Center for Atmospheric Research Mesoscale Model (MM5), both models producing a similar overprediction of precipitation, particularly on the immediate lee of the cascade crest. For KY, the excess leeside precipitation appeared to be strongly related to large quantities of snow being advected over the crest and then carried downward in regions of strong downward vertical motion (strengthened by sublimational cooling), where it then melted to rain, rather than being converted to graupel in the cloud water pockets on FIG. 8. As in Fig. 7, but for the MY-2 (1 km) simulation.

10 634 M O N T H L Y W E A T H E R R E V I E W VOLUME 138 FIG. 9. As in Fig. 7, but for the MY-1 (1 km) simulation. Note that the shading interval for snow is different from that in Fig. 7. the windward side where it would have precipitated earlier due to the larger fall velocities of graupel. G05a,b made a similar argument regarding their simulations. The same mesoscale model was used for the KY and MY-3 runs. Thus, the similarity of the KY and Reisner-2 simulations strengthens the claim made in Part I that, owing to the similarities of the large-scale features in the GEM and MM5 simulations, the differences in the MY-3 and G05 s Reisner-2 runs can be accounted for largely by differences between the microphysics schemes, and not the use of different models or their configurations. The precipitation and hydrometeor fields from MY-1 were quite different from both the KY and Reisner-2 simulations. Variation in the results from different singlemoment schemes is not surprising, but the fact that the MY-1 simulations were closer to MY-3 and MY-2, in terms of precipitation, than to KY is of some interest. It suggests that the differences between MY-3 and the simulations with Reisner-2 and KY cannot simply be attributed to the use of multiple moments versus one moment. The fact that MY-1 produced a QPF with a realistic spatial distribution for this case (with no leeside FIG. 10. As in Fig. 7, but for the KY (1 km) simulation. Note that (b) is for rain only (since there is no pristine ice category in KY).

11 FEBRUARY 2010 M I L B R A N D T E T A L. 635 TABLE 2. Observed cloud liquid water vs model Q c along P-3 flight legs. Model values for the five legs are taken at 2300, 0000, 0000, 0000, and 0100 UTC, respectively. Nonbracketed [bracketed] numbers denote mean [peak] values (g m 23 ) along flight legs. Valley Windward Lee Flight leg Leg 1 Leg 2 Leg 3 Leg 4 Leg 5 Elev (m) (pressure level, hpa) 2000 (775) 2500 (725) 3450 (650) 4000 (600) 3100 (675) Obs avg [peak] (g m 23 ) 0.14 [0.40] 0.26 [0.50] 0.20 [0.25] 0.12 [0.15] 0.04 [0.10] MY-3 avg [peak] (g m 23 ) 0.09 [0.40] 0.06 [0.19] 0.00 [0.00] 0.00 [0.00] 0.01 [0.14] MY-2 avg [peak] (g m 23 ) 0.11 [0.55] 0.06 [0.17] 0.00 [0.00] 0.00 [0.00] 0.01 [0.07] MY-1 avg [peak] (g m 23 ) 0.11 [0.32] 0.09 [0.34] 0.02 [0.17] 0.01 [0.10] 0.00 [0.00] KY avg [peak] (g m 23 ) 0.31 [0.47] 0.40 [0.71] 0.30 [0.55] 0.03 [0.30] 0.00 [0.03] overprediction), similar to MY-3 and MY-2, suggests that other differences between the MY-x, KY,andReisner-2 schemes, besides the number of moments, are important for the QPF. While a detailed examination of all of the differences between these BMSs is beyond the scope of this paper, the large differences between the simulated snow mass quantities of the MY-1 simulation and those of the other runs, despite similar forcing, merit investigation. This is discussed section 4d, followed by an examination of the leeside precipitation. d. Depositional growth of snow The peak values of snow mass contents in the cross sections in Figs for MY-3, MY-2, MY-1, and KY are.1.5, ;2.0, between , and.1.5 g m 23, respectively The lower snow mass in MY-1 (Fig. 9d) and the similarity in quantity among MY-3, MY-2, and KY (Figs. 7d, 9d, and 10d) can be partly explained by examining the depositional growth rates from the various schemes. These rates result directly from the representation of the snow size distributions. Except for riming at lower levels, snow mass increases mainly from vapor deposition. In MY-1, therefore, there were either lower deposition rates on average and/or the snow sedimented faster through the regions of supersaturation, thus having less time to acquire mass (even if the deposition rate is large). The equation for the depositional growth rate (mixing ratio tendency) used in MY-x and KY, which all assume spherical particles, can be expressed as " VD vs 5 1 AB i 2p(S i 1)N 0,s VENT s # L s L f K a R y T 2 (CL cs 1 CL rs ), (2) where AB i is the thermodynamic growth parameter and depends on the ambient temperature and pressure, S i is the saturation ratio with respect to ice, VENT s is the ventilation factor and depends on the size distribution parameters, fall speed parameters, and ventilation coefficients for snow [see Eq. (36) in MY05b]. The second term in the brackets accounts for the decrease in the deposition rate as a result of latent heat effects from the accretion of cloud water (CL cs ) and rain (CL cr ) and their freezing. L s, L f, K a, R y, and T are the latent heats of vaporization and fusion, the thermal conductivity of air, the gas constant for water vapor, and the ambient air temperature, respectively. In the multimoment schemes (MY-2 and MY-3) the intercept parameter is computed by 1 N 0,s 5 N Ts G(1 1 a s ) l11a s s, (3) where N Ts is the total number concentration, l s is the slope parameter, and a s is the spectral dispersion parameter. TABLE 3. Observed ice mass content vs model Q s along Convair-580 flight legs. Model values for the four legs are taken at 2300, 0000, 0000, and 0100 UTC, respectively. Nonbracketed [bracketed] numbers denote mean [peak] values (g m 23 ) along flight legs. Flight leg Leg a b Leg c d Leg e f Leg g h Elev (m) (pressure level, hpa) 6000 (450) 5300 (500) 4900 (525) 4300 (625) Obs avg (g m 23 ) MY-3 avg [peak] (g m 23 ) 0.37 [0.59] 0.58 [0.67] 0.65 [0.79] 0.85 [1.17] MY-2 avg [peak] (g m 23 ) 0.31 [0.54] 0.50 [0.69] 0.54 [0.71] 0.79 [1.06] MY-1 avg [peak] (g m 23 ) 0.26 [0.45] 0.28 [0.36] 0.37 [0.44] 0.48 [0.86] KY avg [peak] (g m 23 ) 0.35 [0.38] 0.66 [1.14] 0.69 [1.06] 1.02 [1.30]

12 636 M O N T H L Y W E A T H E R R E V I E W VOLUME 138 TABLE 4. Observed ice mass content vs model Q s 1 Q g along P-3 flight legs. Model values are taken at 0100 UTC. Nonbracketed [bracketed] numbers denote mean [peak] values (g m 23 ) along flight legs. Flight leg Lee Win 1 Win 2 Elev (m) (pressure 4000 (625) 3500 (650) 2500 (725) level, hpa) Obs avg [peak] (g m 23 ) 0.10 [0.25] 0.40 [0.55] 0.25 [0.47] MY-3 avg [peak] (g m 23 ) 0.34 [0.74] 0.96 [1.40] 0.90 [1.22] MY-2 avg [peak] (g m 23 ) 0.29 [0.72] 0.87 [1.35] 0.86 [1.12] MY-1 avg [peak] (g m 23 ) 0.20 [0.44] 0.58 [0.92] 0.62 [0.88] KY avg [peak] (g m 23 ) 0.58 [0.65] 1.21 [1.49] 1.46 [1.67] 1) RESIDENCE TIME IN GROWTH ZONE Before examining the deposition rates, we determine if the differences in total growth are due in part to different residence times in the growth zones by inspecting the mass-weighted fall velocities of snow from the various runs. Figure 11 shows the instantaneous bulk snow fall velocities, V Qs, at 0000 UTC from the 4-km simulations, calculated by V Qs 5 ga s G(1 1 d s 1 a s 1 b s ) G(1 1 d s 1 a s ) 1 l b s s, (4) where g is the air density correction factor, a s and b s are the fall speed parameters, and d s is the exponent in the mass diameter relation. The snow in MY-1 (Fig. 11c) sediments more slowly than in the other runs in general, except for a region between approximately 400 and 550 hpa where it is faster than MY-3 (Fig. 11a) and MY-2 (Fig. 11b). Thus, while different sedimentation rates may be a contributing factor, the lower snow mass quantities in MY-1 do not appear to be entirely a result of shorter residence times in the growth zones (i.e., regions that are supersaturated with respect to ice). Similarly, the snow fall velocities are the highest in KY, while its mass values are similar to MY-2 and MY-3 and higher than MY-1, rather than being correspondingly lower. Thus, while some of the differences in the snow mass contents illustrated in Figs. 7 9 may be partly due to different sedimentation rates, differences in the deposition rates are certainly a contributing factor. 2) INSTANTANEOUS GROWTH RATES At specific points in space and time in the simulations, the values of the prognostic variables (mass, number concentration, and reflectivity) that determine the snow size distribution parameters may be different. This makes direct comparison of the size distributions, and the resulting growth rates, difficult to interpret since the different rates result from both different values of the prognostic variables and different assumptions in computing the distribution parameters used in (3). To eliminate the variability due to different predicted values, we compare size distributions for each scheme and the corresponding growth rates that would be present given the same values of the prognostic moments. For this comparison, the snow size distributions for each scheme are plotted (Figs. 12 and 13), based on the distribution parameters computed from two sets of specified values of the mixing ratio (used for all schemes), total number concentration (used for MY-2 and MY-3 only), and reflectivity (used for MY-3 only), as well as temperature and pressure. The specific assumptions and equations used can be found in MY05a and KY97. Since the distribution parameters for KY have an additional dependence on S i (discussed below), we first examine the size distributions for MY-x, which depend only on the prognostic snow variables. The size distributions for the MY-x schemes are shown for two sets of variables in Figs. 12a,b, respectively. The corresponding depositions rates (VD vs ), indicated in the figures, are calculated from (2) assuming saturation with respect to water to estimate S i and prescribing the riming rate to be zero. For comparison, we have also included in the figure the size distributions and growth rates that would have resulted for the two-moment configuration with a prescribed inverse-exponential distribution (a s 5 0, rather than diagnosed) referred to as MY-2_fixed. For the inverse-exponential distributions, MY-1 has a smaller intercept (N 0,s ) compared to MY-2_fixed as well as a lower deposition rate. This is consistent with (2) and with what would be expected physically for two populations of particles with the same total mass but different total number concentrations. (For MY-1 and MY-2_fixed, VENT s also varies, but only slightly compared to the differences in N 0,s.) In comparison, MY-2 and MY-3 both have narrower spectra, corresponding to larger values of a s, and larger growth rates. While the physical meaning of N 0,s as well as the dimensions change with increasing a s for gamma distributions, the dimensions of N 0,s 3 VENT s in (2) remain the same. It must be emphasized that for MY-x in Fig. 12 it is only the differences in the size distributions that lead to different deposition rates. Thus, it is evident that VD vs is strongly influenced by the number concentration of smaller particles; that is, those in the size range of approximately m ( mm) for this example. This is consistent with the fact that for snow particles represented as spheres (as in the MY-x and KY parameterizations), VD vs is directly proportional to the moment 2 1 b s of the size distribution, where b s is the

13 FEBRUARY 2010 M I L B R A N D T E T A L. 637 FIG. 11. Mass-weighted bulk fall velocities (m s 21 ) for snow at 0000 UTC for the 4-km simulations with (a) MY-3, (b) MY-2, (c) MY-1, and (d) KY. Contour and shading intervals are 0.2 m s 21. Location of cross sections is indicated by solid arrow in Fig. 2a. fall speed parameter of snow (0.42 [MY-x] and 0.25 [KY]). 3 Because of this dependence on a lower moment, the value of VD vs is strongly influenced by the number concentration of small particles, though not necessarily the smallest particles. A similar analysis for the KY scheme has the added complication that the snow size distribution parameters themselves are dependent on the saturation ratio with respect to ice. This is because the total number concentration is approximated at each point in space and time using the parametric equation from Meyers et al. (1992): N Ts exp[12.96(s i 1) 0.639]. (5) This value is then used along with the mixing ratio to determine N 0,s and l s, with a fixed a s 5 0. We look first at the KY size distributions and deposition rates computed using the same S i values that were used in Fig. 12. These are shown in Fig. 13, indicated by the thin dashed lines, with a corresponding VD vs kg kg 21 s 21. For the purpose of direct comparison, the ventilation and fall speed coefficients of MY-x were used for these calculations. The concentration of particles smaller than 3 For the diffusional growth of a single sphere, whose capacitance is thus equal to half its diameter D, the growth rate is proportional to D times the Reynolds number, where the latter is proportional to D 11b. The bulk diffusional growth rate for the entire population of particles is therefore proportional to the moment 2 1 b. (See KY97 and MY05a,b for details) m and the values of VD vs are smaller for KY (Fig. 13) than for the corresponding MY-x distributions (Fig. 12). The deposition rates in the KY simulations would be smaller than in all of the MY-x runs for these values. However, the exponential dependency of S i for N Ts in (5) means that for the same snow mass located slightly higher in elevation, thus at a colder temperature, in a water-saturated environment, the small increase in S i leads to larger values of N Ts, N 0,s, and thus VD vs. This is illustrated in Fig. 13, where the size distributions for various larger values of the saturation ratio are plotted and the corresponding deposition rates are indicated. For example, S i implies a saturation ratio that is 20% larger than the value used in Fig. 12 (assumed to be 1.08). The size distributions and deposition rates in KY are clearly very sensitive to S i. In fact, N 0,s changes by nearly one order of magnitude for every 10% increase in S i, corresponding to a decrease in temperature of approximately 108C (assuming water saturation). In general, deposition rates increase quickly with height for the KY simulations due to this strong (double) dependency on S i. e. Leeside precipitation The concentrated zone of excessive precipitation in the immediate lee of the cascades appeared in KY (Figs. 2 and 3) and G05a,b s simulations (see Fig. 16 in Garvert et al. 2007), absent from the MY-x runs (Figs. 2 and 3), is of interest. Inspection of the equations in the schemes

14 638 M O N T H L Y W E A T H E R R E V I E W VOLUME 138 FIG. 12. Snow size distributions as represented by the various MY-x schemes for two sets of prescribed values of mass, total number concentration, and reflectivity. Depositional growth rates (VD vs ), assuming saturation with respect to water, are indicated for each scheme. and sensitivity tests suggest two potential contributing factors for this conspicuous difference between the runs. 1) LATENT HEATING EFFECT ON THE DEPOSITION RATE FIG. 13. Snow size distribution for the KY scheme, corresponding to the values of the mass contents used in Figs. 10a,b, respectively, for various supersaturation values (e.g., S i indicates a supersaturation that is 20% larger than the supersaturation value used in the corresponding panels in Fig. 12). The corresponding depositional growth rates (VD vs ) are indicated in the lower-left corners. The first contributing factor is related to the role of the second term in the brackets in (3), which reduces the deposition rate because of an increase in the saturation mixing ratio resulting from latent heat release during the freezing of accreted cloud and rain water. A sensitivity test (referred to as MY-2_S1) was performed using the MY-2 scheme with this term in (3) shut off. Vertical cross sections of the instantaneous (0000 UTC) growth decay rates for snow by diffusion (VD vs ) and accretion of cloud (CL cs ) for the control run (MY-2) and the sensitivity run (MY-2_S1) are shown in Figs. 14a,b. It is apparent from inspection that in regions where accretion is appreciable, the depositional growth rate is greatly reduced. For example, in MY-2, there is an abrupt cutoff 4 of VD vs immediately below the region of relatively large CL cs near the main mountain crest on the upwind side (at approximately 650 hpa; Fig. 14a), while in MY-2_S1 (Fig. 14b) the field of positive VD vs extends down to approximately 750 hpa, well into the region of large CL cs. It is also apparent in the control run that the reduced deposition rates lead to less depletion of water vapor by snow leaving more available for condensation and thus larger rates of accretional growth 4 Note, large accretion rates will never result in a negative deposition rate in a supersaturated environment; if the second term in (2) dominates and S i. 0, the diffusional growth rate is zero.

15 FEBRUARY 2010 M I L B R A N D T E T A L. 639 of snow. The net effect, however, is for there to be less snow at lower levels. This can be seen in Fig. 14c, which depicts a vertical cross section of the difference in snow mass between MY-2_S1 and MY-2. The effect of shutting off term 2 in (2) is ultimately to produce more snow at lower levels and less at higher levels. As a result, the precipitation pattern is altered so as to produce a distinct increase in the leeside precipitation (Fig. 15a). This increase in MY-2_S1 coincides closely with the pronounced leeside precipitation for the KY runs (Figs. 2 and 3). This is consistent with the fact that the KY scheme does not include the latent heat effect term in (2). 5 It would therefore appear that the difference in leeside precipitation between the MY-x and the KY simulations could be at least partially accounted for by the inclusion of this second term. On the other hand, for G05a,b s simulations the latent heat effect term appears to have been added to the Reisner-2 BMS with the modifications of Thompson et al. (2004) since the original RRB. Thus, unless this modification was not included in G05a,b s simulations, this would not account for the differences in the leeside precipitation between the MY-x and the Reisner-2 runs. 2) COMPUTATION OF THE SNOW MELTING RATE FIG. 14. Depositional growth rate (VD vs ; kg kg 21 s 21 ; thick contours) and accretional growth rate (CL cs ; thin contours/ shading) for (a) MY-2 and (b) MY-2_S1 at 0000 UTC. Contours for VD vs are every kg kg 21 s 21 ; contours/shading for CL cs are every kg kg 21 s 21. (c) Difference in snow mass contents, Q s, between MY-2_S1 and MY-2 at 0000 UTC. Contours are 0.1, 0.3, 0.5, 1.0, 1.5, and 2.0 g m 23. Dashed contours denote negative values. Location of cross sections is indicated by solid arrow in Fig. 2a. 5 The KY97 article describing the scheme contains this term in the equation for the diffusional growth of snow (ice). However, in the version of the KY code in the official GEM model used for the simulations in this paper, this term is not present. The second potential factor is the treatment of the melting of snow. In MY-x, the melting rate is computed explicitly while in KY snow is assumed to melt instantly to rain as soon as the ambient air temperature is greater than 08C. This is evident in Fig. 10 where the 08C isotherm essentially delineates the time-averaged snow and rain fields due to the instantaneous melting. The effect of this is to concentrate the leeside precipitation since rain sediments much faster than snow. In MY- x, on the other hand, the precipitation exists as slowly falling snow for a longer period and is thus transported farther downstream, away from the immediate lee of the mountain. A second sensitivity test (referred to as MY-2_S2) was performed with the MY-2 scheme in which all of the snow was forced to melt instantaneously if T. 08C. The difference in accumulated precipitation between MY-2_S2 and MY-2 is shown in Fig. 15b. The change in the snow melting rate results in an increase in the leeside precipitation, though with less pronounced an effect than the latent heat effect term discussed above. Although the Reisner-2 scheme computes an explicit melting rate of snow (RRB), similar to MY, Fig. 3 in G05b depicts a nearly identical pattern of snow and rain to KY (Fig. 10), with virtually no overlap and separated by the 08C isotherm. This suggests that despite the inclusion of the explicit melting rate, the snow appeared to be melting very abruptly in the G05a,b simulations, as in KY, and may partly account for the similar patterns of large precipitation quantities concentrated in the immediate lee of the cascades. 5. Conclusions Sensitivity experiments were conducted to examine the importance of the number of predicted moments in a BMS for the simulation of the December 2001 case of orographically enhanced precipitation, which was well observed during the IMPROVE-2 campaign. Simulations were performed with 4- and 1-km horizontal grid-spacings using triple-, double-, and single-moment versions of the MY05a,b scheme plus the single-moment

16 640 M O N T H L Y W E A T H E R R E V I E W VOLUME 138 FIG. 15. Differences in 18-h accumulated precipitation (mm) for (a) MY-2_S1 2 MY-2 and (b) MY-2_S2 2 MY-2. Contours are every 5 mm (dashed denotes negative values). Shading denotes orographic height, with interval of 500 m. KY97 scheme, with the focus on the 2-h period of heavy stratiform precipitation, when the hydrometeor fields were quasi-steady and for which in situ microphysical measurements were available. There was little difference between the triple- and double-moment runs, both exhibiting realistic spatial distribution of the precipitation, though systematically overpredicted in quantity, but too much snow mass and too shallow cloud water pockets aloft. Greater sensitivity was found to the reduction of the scheme to single moment, which resulted in an increased precipitation bias and an upwind shift in the precipitation pattern, but a snow cloud mass balance conforming more closely to the observations. The greatest sensitivity of the simulations was found to the particular single-moment scheme used. For the KY scheme, a pronounced band of overpredicted precipitation occurred on the immediate lee side of the Cascade crest, unlike in the single-moment MY scheme. The singlemoment runs also had very different hydrometeor mass fields aloft, with MY producing much less snow than KY. Two additional sensitivity tests using the doublemoment MY scheme indicated that the leeside overprediction problem exhibited by KY (and G05a,b) but absent from any of the MY-x runs was likely due to the combined effects of the absence (in the KY scheme) of the latent heat effect term in the equation for diffusional growth of snow and the assumption of instantaneous melting of snow. Suppression of the latent heat effect term in the MY scheme and imposing instantaneous melting both resulted in simulations with a sharp enhancement of precipitation on the immediate lee. The results of this study may suggest that the snow mass field can be better simulated by a single-moment scheme. However, the multimoment configurations used were largely unconstrained in terms of the snow size distribution. As indicated in section 4, unrealistically large values of N 0,s for a double-moment scheme (with an inverse-exponential snow size distribution) can lead to excessively large depositional growth rates. Sensitivity tests were conducted (not shown) whereby the double-moment scheme was run with upper limits imposed on N 0,s, similar to the approach in Reisner et al. (1998), and produce simulated snow and cloud mass fields that were much closer to other observations. Thus, the multimoment configurations can easily be calibrated to improve the cloud snow mass balance aloft. Even despite the incorrect cloud snow balance in the unconstrained multimoment runs, the precipitation patterns and scatterplots indicate at least as good QPFs from the multimoment configurations as the single-moment MY. There are also other advantages to the multimoment treatment of snow. For example, as shown in Part I the vertical distribution of the mean-mass snow diameters compared favorably to the in situ observations. This was due to a combination of size sorting and aggregation, which are each explicitly simulated in a multimoment scheme but whose combined effects can only be mimicked in a single-moment scheme through use of a height-dependent diagnostic relation for N 0,s. The proper treatment of these processes may be important for certain applications, such as process studies, simulations where the computations of radiative transfer through clouds is more important, or the exploitation of relations for the bulk snow density as function of the mean-mass diameter. In all of the simulations in this study as well as those of G05a,b, the snow mass fields were overpredicted to various degrees compared to the mass contents inferred by in situ measurements. In addition to a possible moisture bias in the models and treatment of the snow size distributions, another possible source of error common to all microphysics schemes may lie in the use of the electrostatic capacitance analogy for depositional growth (Pruppacher and Klett 1997). Recent theoretical calculations of crystal capacitances by Westbrook et al. (2008) using synthetic aggregates indicate that the geometric capacitance for spherical particles, used in most bulk schemes, is a factor of 2 too large. This is in agreement with in situ aircraft measurements of snow growth (Field et al. 2006). Furthermore, recent laboratory measurements have shown that because of irregularities in the shapes of real ice crystals, the electrostatic analogy overestimate diffusional growth by a factor of 2 8 or more (Bailey and Hallett 2004, 2006). The use of experimentally determined effective capacitances for ice crystal categories in microphysics schemes in general may be a way of improving the simulation of the depositional growth.